Based on point P(0,16), we substitute in the parabola to find a.
16=a(0-3)^2-2 => a=(16+2)/9=2
so the parabola is
y=2(x-3)^2-2 ..........................(1)
Solve for zeroes of (1);
0=2(x-3)^2-2 => (x-3)^2=1 => x=2 or x=4
Now the line passes through (0,16), (4,0) => y,x intercepts are 16 & 4.
Using the symmetric form
x/4+y/16=1
4x+y=16 => y=16-4x
